Papers
Authors
Leo Brewin
Abstract
A new lattice based scheme for numerical relativity will be presented. The
scheme uses the same data as would be used in the Regge calculus (eg. a
set of leg lengths on a simplicial lattice) but it differs significantly
in the way that the field equations are computed. In the new method the
standard Einstein field equations are applied directly to the lattice.
This is done by using locally defined Riemann normal coordinates to
interpolate a smooth metric over local groups of cells of the lattice.
Results for the time symmetric initial data for the Schwarzschild
spacetime will be presented. It will be shown that the scheme yields
second order accurate estimates (in the lattice spacing) for the metric
and the curvature. It will also be shown that the Bianchi identities play
an essential role in the construction of the Schwarzschild initial data.